Question

Question No. 112 :

The height of a tree is 30 m. The upper part of the tree, broken over by the wind makes an angle of 30 degree with the ground. Find the length of the upper broken part. Also find the horizontal distance from the foot of the tree to the point where the top meets the ground.

Answer 1

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Answer 2

$\huge\textbf{Solution}$


Let the total height of tree be h. (AB)

Distance of tree from bottom to bent part is x. (BC)

Now

In ∆ ABC

$\dfrac{AB}{BC}$ = tan 30°

$\dfrac{h}{x}$ = $\dfrac{1}{\sqrt{3}}$

x = h√3 .....(1)

Also;

$\dfrac{BC}{AC}$ = cos 30°

$\dfrac{BC}{AC}$ = $\dfrac{\sqrt{3}}{2}$

$\dfrac{x}{30\:-\:h}$ = $\dfrac{\sqrt{3}}{2}$

2x = (30 - h)√3

2h√3 = 30√3 - h√3 [from (1)]

2h√3 + h√3 = 30√3

3h√3 = 30√3

3h = 30

h = $\dfrac{30}{3}$

h = 10 m

Put value of h in (1)

x = h√3

x = 10√3 m